Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework. Specifically,
we learn local metrics optimized from parametric generative models. These are then used as base kernels to construct a global kernel that minimizes a discriminative training criterion. We consider both linear and nonlinear combinations of local metric kernels. Our empirical results show that these combinations significantly improve performance on classification tasks. The proposed learning algorithm is also very efficient, achieving order of magnitude speedup in training time compared to previous discriminative baseline methods.
